The American “indians” also had the swastika. It is a simple enough symmetrical design to be independently designed around the world, I’m sure.
But if you believe in Panspermia, the process where the more people breed the more room they need, you understand as they spread they took their traditions with them. Worldwide. But unscrupled people always pop up and twist these traditions into some perversion for their own nefarious purposes. Kinda sorta like when I was a little kid and we had Christmas. But now we have The Holiday Season. ;-)
Sure, but it is ironic and quite the coincidence that on two continents, thousands of miles apart, the same symbol, albeit simple, as you say sprang up.
But simplicity works, witness the cross in Christianity.
And in Islam, the sword!